document.write( "Question 1036557: 5 men are hired to complete a job. If one more man is hired, the job can be completed 8days earlier. Assuming that all men work at the same rate, how many more men should be hired so that the job can be completed 28 days earlier? \n" ); document.write( "
Algebra.Com's Answer #651246 by Edwin McCravy(20056)\"\" \"About 
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...Assuming that all men work at the same rate,
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document.write( "Let the rate of 1 man be r.\r\n" );
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\n" ); document.write( "5 men are hired to complete a job.
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document.write( "So the rate of the 5 men is 5r \r\n" );
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document.write( "Since time = production/rate = (1 job)/(5r),\r\n" );
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document.write( "The 5 men could do the job in 1/(5r) days\r\n" );
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\n" ); document.write( "If one more man is hired,...
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document.write( "That makes 6 men, whose rate is 6r.\r\n" );
document.write( "Since time = production/rate = (1 job)/(6r),\r\n" );
document.write( "The 6 men could do the job in 1/(6r) days\r\n" );
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\n" ); document.write( "the job can be completed 8days earlier.
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document.write( "So 1/(6r) is 8 days less than 1/(5t), or\r\n" );
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document.write( "1/(6r) = 1/(5r) - 8\r\n" );
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document.write( "Multiply thru by LCD = 30r\r\n" );
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document.write( "    5 = 6 - 240r\r\n" );
document.write( "   -1 = -240r\r\n" );
document.write( "1/240 = r  <-- the rate of one man\r\n" );
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document.write( "That makes the rate of 5 men be 5/240,\r\n" );
document.write( "or 1/48, that's 1 job per 48 days, so the \r\n" );
document.write( "5 men could finish 1 job in 48 days.  \r\n" );
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\n" ); document.write( "how many more men should be hired so that
\n" ); document.write( "the job can be completed 28 days earlier
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document.write( "Let the number of men that must be hired be n\r\n" );
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document.write( "Then there will be 5+n men working\r\n" );
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document.write( "So the rate of 5+n men is (5+n)r = (5+n)(1/240) = (5+n)/240 \r\n" );
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document.write( "Since time = production÷rate = (1 job)÷((5+n)/240) = 1×(240/(5+n) =\r\n" );
document.write( "          240/(5+n)\r\n" );
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\n" ); document.write( "...the job can be completed 28 days earlier
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document.write( "So 240/(5+n) is 28 days less than the 48 days it would\r\n" );
document.write( "take the 5 men, or 20 days.\r\n" );
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document.write( "240/(5+n) = 20\r\n" );
document.write( "      240 = 20(5+n)\r\n" );
document.write( "      240 = 100+20n\r\n" );
document.write( "      140 = 20n\r\n" );
document.write( "        7 = n\r\n" );
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document.write( "So 7 more men must be hired.\r\n" );
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document.write( "Edwin
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